Question

Giải hệ \(\left\{{}\begin{matrix}x^2y+2x^2+3y-15=0\\x^4+y^2-2x^2-4y-5=0\end{matrix}\right.\)

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}2x^2y+4x^2+6y-30=0\\x^4+y^2-2x^2-4y-5=0\end{matrix}\right.\)

\(\Rightarrow x^4+2x^2y+y^2+2x^2+2y-35=0\)

\(\Rightarrow\left(x^2+y+1\right)^2-36=0\)

\(\Rightarrow\left[{}\begin{matrix}x^2+y+1=6\\x^2+y+1=-6\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x^2=5-y\\x^2=-7-y\end{matrix}\right.\)

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